The asymmetric simple exclusion process

Abstract:

The asymmetric simple exclusion process (ASEP) is arguably the simplest generalization of simple walk on the integer lattice to interacting random walkers on the integer lattice. This lecture will explain why ASEP is an integrable model (Bethe Ansatz solvable) and how exact formulas in ASEP lead to the distribution of the height function for the Kardar-Parisi-Zhang (KPZ) equation. We will conclude with recent work on blocks and gaps in ASEP; in particular, under KPZ scaling. No prior knowledge of ASEP will be assumed.